Experimental evidence has been published by Thurber (MSc thesis University of Tulsa, 1988, p. 61) that led him to state that the settling velocity predicted by Stokes' law in the case of a decanter has to be reduced. He found a crude empirical expression saying that at shallow pond depths (<0.125 ft) and high processing rates “>75% of “maximum rate” the settling velocity was reduced by a factor 0.3 found from regression analysis. At processing rates greater than 50% of the “maximum rate” a reduction factor of 50% was found.
As it is generally known that reducing turbulence in a decanter will lower the cut point, and since (apart from Thurber's observations) no published analytical approach exists that can help taking into account the influence of turbulence in the design and optimization of decanter operation, a new analytical method has been found to fill this gap in knowledge. The present invention models this analytical method, but it will be obvious that more intricate geometries than the one described here can better be dealt with by Computational Fluid Dynamics. The underlying principle remains the same, that is finding areas of turbulence by applying some criterion based on Reynolds number.
As is described in advanced engineering text books (see e.g. Coulson and Richardson), entry of a fluid from a differently shaped reservoir into a pipe or slot will result in an initial zone where turbulent flow prevails. After a certain distance, the entry length, the fluid has developed a laminar velocity profile, see FIG. 1. This transition is marked by a thickening of a boundary layer, the thickness of which is proportional to the square root of the distance from the entry point. The laminar region is therefore surrounded by a parabolic boundary. In the case of slot flow, fully established laminar flow is achieved when the boundary layers meet each other.
Collins and Schowalter have studied these effects for non-Newtonian fluids in two papers dealing respectively with entry into a pipe and a channel (A.I.Ch.E.Journal, 1963). For the purposes of the invention described herein, it is sufficient to summarize their results by stating that the ratio Entry Length/Hydraulic Diameter multiplied by Reynold's number is equal to a constant value. For pipes this value is 0.05 and for slots this value is 0.0088.
The conclusions from Thurber's thesis suggest that a relationship of the same form as found by Collins and Schowalter can be used to describe turbulence in the pond of a decanting centrifuge. It would be an improvement in the art to develop a model incorporating the effects of both turbulent and laminar flow. Such a model further accounting for the formation laminar boundary layer within the pond of a decanting centrifuge could be used to improve centrifuge design as well as to more accurately predict the cut point function of a centrifuge.